Rate of approach to the steady state for a diffusion-convection equation on annular domains

In this paper, we study the asymptotic behavior of global solutions of the equation ut = �u + e jr uj in the annulus Br,R, u(x, t) = 0 on @Br and u(x, t) = M � 0 on @BR. It is proved that there exists a constant Mc > 0 such that the problem admits a unique steady state if and only